True Strain Calculator

Enter your engineering stress and engineering strain values to get the corresponding true stress and true strain — the actual internal stress and deformation your material experiences as it deforms. The True Strain Calculator converts nominal (engineering) stress-strain values into their true counterparts using the standard plasticity formulas, accounting for the changing cross-sectional area during deformation.

Dimensionless ratio: (change in length) / (original length). Enter as a decimal (e.g. 0.15 for 15%).

MPa

Nominal stress = Force / Original cross-sectional area.

Results

True Strain (εₜ)

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True Stress (σₜ)

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Difference (εₜ − ε)

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Stress Increase (σₜ − σ₀)

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Engineering vs True Stress-Strain Comparison

Results Table

Frequently Asked Questions

What is the difference between true stress and engineering stress?

Engineering stress (nominal stress) is calculated by dividing the applied force by the original cross-sectional area of the specimen, which remains constant throughout the calculation. True stress accounts for the actual, instantaneous cross-sectional area at each point of deformation — as a material stretches, its cross-section narrows, so the true stress is always higher than engineering stress beyond the elastic region.

How do I calculate true strain from engineering strain?

True strain (εₜ) is calculated from engineering strain (ε) using the formula: εₜ = ln(1 + ε), where ln is the natural logarithm. For example, an engineering strain of 0.15 gives a true strain of ln(1.15) ≈ 0.1398. True strain is always slightly smaller than engineering strain for the same deformation.

How do I calculate true stress from engineering stress?

True stress (σₜ) is obtained from engineering stress (σ₀) and engineering strain (ε) using: σₜ = σ₀ × (1 + ε). This relationship assumes constant volume (incompressible plastic deformation), which means the decrease in cross-sectional area is accounted for by the factor (1 + ε).

How do I convert the engineering strain 0.05 to true strain?

Plug the value into the formula εₜ = ln(1 + ε). For ε = 0.05: εₜ = ln(1.05) ≈ 0.04879. The difference is small at low strains but becomes significant at large plastic deformations (strains above ~0.1).

Why do engineers use true stress-strain instead of engineering stress-strain?

True stress-strain values reflect the actual material behavior during plastic deformation, making them essential for accurate finite element analysis (FEA), metal forming simulations, and failure analysis. Engineering stress-strain is adequate for elastic (small-deformation) analysis, but true values are required once a material yields and undergoes significant shape change.

Does the true stress-true strain conversion apply to all materials?

The formulas εₜ = ln(1 + ε) and σₜ = σ₀(1 + ε) are derived assuming volume conservation — valid for metals undergoing plastic deformation. For brittle materials (ceramics, some polymers) that fracture with little plasticity, or for rubber-like materials with large elastic strains, different constitutive models may be more appropriate.

What is necking and how does it affect true stress calculations?

Necking is the localized reduction in cross-sectional area that occurs after the ultimate tensile strength is reached. Beyond this point, the simple conversion formula σₜ = σ₀(1 + ε) becomes inaccurate because strain is no longer uniform — the local strain in the neck is much higher than the average engineering strain. Specialized correction factors (like the Bridgman correction) are needed for post-necking analysis.

Is true strain always larger or smaller than engineering strain?

True strain is always smaller than engineering strain for the same physical deformation. This is because ln(1 + ε) < ε for all positive values of ε. The gap between them grows as strain increases — at small strains (e.g. ε < 0.05) they are nearly identical, but at large strains they diverge considerably.

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